Analytical and numerical solutions for a special nonlinear equation

Hossein Sahebi Fard, Elham Dastranj (), Reza Hejazi () and Amin Jajarmi ()
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Hossein Sahebi Fard: Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Elham Dastranj: Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Reza Hejazi: Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Amin Jajarmi: Department of Electrical Engineering, University of Bojnord, Bojnord, North Khorasan, Iran

International Journal of Financial Engineering (IJFE), 2024, vol. 11, issue 01, 1-24

Abstract: In the most of the option price dynamics in the financial markets, the transaction cost of option is ignored. Considering the transaction costs will lead to the emergence of models with nonlinear PDE. In this paper, transaction cost of option in the assumed market is considered, and the resulting dynamic is a nonlinear PDE, whose exact and numerical solutions have been computed in the present paper. To find the exact solution of the cited nonlinear equation, the Lie group algebra method has been used. The numerical solution has been given using the Chebyshev spectral method. In this method, the solution of the considered equation is approximated using Chebyshev polynomials. The convergence of the obtained polynomials to the solution of the differential equation has been shown, as well.

Keywords: Nonlinear Heston model; transaction cost; Lie symmetries; Chebyshev spectral method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S2424786323500573

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